Types of Image Transformation

TELKOMNIKA ISSN: 1693-6930  An Image Registration Method Based on Wavelet Transform and Ant Colony ... Dapeng Zhang 605 complicated and the application has huge restrictions. Instead of directly operating on the image gray, the feature-based method tends to extract control structure in the feature space and realize image registration. With the development of computation intelligence, intelligent algorithms are increasingly used in image registration and play an important influence on the effects and efficiency of the image registration [5]. With the feature-based image registration as the foundation, this paper improves such method by integrating wavelet analysis and ant colony optimization so as to expand the application range of the matching algorithm and make the matching effects more outstanding while preserving its original performance. Taking the mutual information as the similarity measure of the image registration, it can automatically adjust the transformation parameter scopes of coarse registration and refined registration and it has a bright application prospect as a universal fully-automatic image registration method. This paper first explains the principle and mathematical model of image registration as well as the registration method based on features; then it proposes the basic workflow of fully-automatic mutual-information image registration according to wavelet theory and ant colony optimization and its final part is the simulation experiment and analysis. 2. Principles of Image Registration 2.1. Definition and Mathematical Model of Image Registration Image registration is the process to match, overlay or process two or more images of the same scene acquired at different times by different sensors imaging devices under different conditions weather, illumination, camera position and angle and it is a fundamental problem of image processing. Two images of the same scene taken under different imaging conditions may be different in deformation and rotation. Image registration is to make the images with different gray scales and geometric transformation into the images with consistent gray scale and geometry. Assume that the two-dimensional arrays 1 , f x y and 2 , f x y stand for the gray-scale values of the corresponding grid positions in the two images, then there exists such a transformation relation between the two images. 2 1 , , f x y g f h x y  1 In this formula, g is the grayscale or radical transformation function and h refers to the two-dimensional coordinate transformation. According to the property of affine transformation, its affine transformation model is: cos sin sin cos x x x y y y                                    2 In this formula,  , x  and y  are the registration parameters of these two images.

2.2. Types of Image Transformation

The most fundamental problem for all image registration techniques is to find out the proper image transformation or mapping type to match two images correctly. After the consistency of the image feature is established, the matching function is also established. We hope to transform the observance image to make it register with the referenced image. Therefore, the design of mapping function shall consider and get closed to the consistent control points of the observance image and the referenced image as much as possible. 1 Rigid-Body Transformation If the distance between the two points of the first image remains the same when transformed to the second image, then this kind of transformation is called rigid-body transformation. Rigid transform can be decomposed into: translation, rotation and mirror reversal. Its transform formula is as follows:  ISSN: 1693-6930 TELKOMNIKA Vol. 13, No. 2, June 2015 : 604 – 613 606 2 1 2 1 cos sin sin cos x y t x x t y y                                3 In this formula, x t and y t are the translation while  is the rotation angle. 2 Affine Transformation If the transformed straight line in the first image remains the straight line when mapped in the second image and maintain an equilibrium relation, such transformation is called affine transformation. Affine transformation can be divided into linear matrix transformation and translation transformation with a transformation formula as follows: 2 1 2 1 cos sin sin cos x y t x x s t y y                                4 In this formula, x t and y t are the translation;  is the rotation angle and s is the scaling. The more common two-dimensional affine transformation formula is as follows: 13 2 11 12 1 23 2 21 22 1 a x a a x a y a a y                        5 3 Projection Transformation If the transformed straight line in the first image remains the straight line when mapped in the second image but the parallel relationship maintains the same, such transformation is called projection transformation, which can be shown by the linear matrix transformation in high-dimensional space. Its transformation formula is: 11 1 12 1 13 21 1 22 1 23 2 2 31 1 32 1 33 31 1 32 1 33 a x a y a a x a y a x y a x a y a a x a y a           6 4 Non-linear Transformation Non-linear transformation can transform straight line into curve. In the two-dimensional space, it can be expressed by the following formula: , , x y F x y    7 In this formula, F refers to any function form to map the first image to the second image.

2.3. Feature-based Image Registration